beautify an image with reinforcement learning
The purpose of Reinforcement Learning is to maximize some notion of cumulative reward, leading me to the point (1) :
as far as I understand, there is no timesteps in your problem and the "reward" is immediate.
Thus, I don't think reinforcement is suitable here.

On an other hand, in supervised learning, linear regression is the task of approximating a mapping function (f) from input variables (X) to a continuous output variable (y).
It has much in common with your case. If I am not wrong, you are trying to approximate a function that maps image data to (x,y) coordinates
(the "sweet spot"). So, I think regression would be a better way to go for you.

You could either generate a dataset at first, with images data and associated (x,y) coordinates for only spots validated by your function F, and then train a regression predictive model. Or you could train your model with online learning, by generating batch of images and sweet spot coordinates at each step.

Concerning the point (2), it will highly depend on how is made your F function. Since overlapping spots cannot be sweet spots, the simplest would
be to make your F function return 0 for those spots.